How to get blooming effect in cycles without compositing
As Jachym Michal says you can create a box with volumetric. A lighter solution is to fake the glowing with a Layer Weight/Facing node:

Create your object.
Create a sphere that contains your object (here displayed as wireframe) and give it a Subdivision Surface modifier to make it smooth.
Give it the following material, which is a mix between Emission (with the color of your cube) and Transparent, with the Layer Weight as Factor in the Mix Shader.



Of course you can increase the Emission' Strength. Also the node organization can be improved with a second Mix Shader to add more transparency, or you can control the Layer Weight with a ColorRamp, or add noise, etc... And you can scale the sphere on whatever axis you want if the object is a long one.